TSTP Solution File: SWC211+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC211+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:41:43 EDT 2023

% Result   : Theorem 7.89s 1.66s
% Output   : CNFRefutation 7.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  110 (  30 unt;   0 def)
%            Number of atoms       :  466 ( 184 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  551 ( 195   ~; 192   |; 128   &)
%                                         (   6 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :  168 (   0 sgn;  99   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil = X3
                      & nil != X2 )
                    | neq(X0,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(cons(X4,nil),X5) = X3
                            & app(X5,cons(X4,nil)) != X2
                            & ssList(X5) )
                        & ssItem(X4) )
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil = X3
                        & nil != X2 )
                      | neq(X0,nil)
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & app(X5,cons(X4,nil)) != X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      | ~ neq(X1,nil)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f148,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f176,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f186,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f186]) ).

fof(f188,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f189,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f188]) ).

fof(f192,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f192]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ~ neq(X0,nil)
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ~ neq(X0,nil)
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f236,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f99]) ).

fof(f237,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f236]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK8(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK8(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK8(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
        & ssList(sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f240,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
                & ssList(sK9(X0,X1))
                & ssList(sK8(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f237,f239,f238]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f187,f335]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f189,f337]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X3
                      | nil = X2 )
                    & ~ neq(X0,nil)
                    & ! [X4] :
                        ( ! [X5] :
                            ( app(cons(X4,nil),X5) != X3
                            | app(X5,cons(X4,nil)) = X2
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ~ neq(sK53,nil)
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & neq(X1,nil)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X3
                  | nil = X2 )
                & ~ neq(sK53,nil)
                & ! [X4] :
                    ( ! [X5] :
                        ( app(cons(X4,nil),X5) != X3
                        | app(X5,cons(X4,nil)) = X2
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & neq(X1,nil)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X3
                | nil = X2 )
              & ~ neq(sK53,nil)
              & ! [X4] :
                  ( ! [X5] :
                      ( app(cons(X4,nil),X5) != X3
                      | app(X5,cons(X4,nil)) = X2
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & neq(sK54,nil)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X3
              | nil = X2 )
            & ~ neq(sK53,nil)
            & ! [X4] :
                ( ! [X5] :
                    ( app(cons(X4,nil),X5) != X3
                    | app(X5,cons(X4,nil)) = X2
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & neq(sK54,nil)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != X3
            | nil = sK55 )
          & ~ neq(sK53,nil)
          & ! [X4] :
              ( ! [X5] :
                  ( app(cons(X4,nil),X5) != X3
                  | app(X5,cons(X4,nil)) = sK55
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & neq(sK54,nil)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( nil != X3
          | nil = sK55 )
        & ~ neq(sK53,nil)
        & ! [X4] :
            ( ! [X5] :
                ( app(cons(X4,nil),X5) != X3
                | app(X5,cons(X4,nil)) = sK55
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & neq(sK54,nil)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( nil != sK56
        | nil = sK55 )
      & ~ neq(sK53,nil)
      & ! [X4] :
          ( ! [X5] :
              ( app(cons(X4,nil),X5) != sK56
              | app(X5,cons(X4,nil)) = sK55
              | ~ ssList(X5) )
          | ~ ssItem(X4) )
      & neq(sK54,nil)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ( nil != sK56
      | nil = sK55 )
    & ~ neq(sK53,nil)
    & ! [X4] :
        ( ! [X5] :
            ( app(cons(X4,nil),X5) != sK56
            | app(X5,cons(X4,nil)) = sK55
            | ~ ssList(X5) )
        | ~ ssItem(X4) )
    & neq(sK54,nil)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).

fof(f356,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f240]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f440,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f470,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f494,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f495,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f520,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f521,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f522,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f523,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f525,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f528,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f548,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f347]) ).

fof(f551,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f553,plain,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    ! [X4,X5] :
      ( app(cons(X4,nil),X5) != sK56
      | app(X5,cons(X4,nil)) = sK55
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f555,plain,
    ~ neq(sK53,nil),
    inference(cnf_transformation,[],[f347]) ).

fof(f557,plain,
    ~ neq(sK55,nil),
    inference(definition_unfolding,[],[f555,f552]) ).

fof(f558,plain,
    neq(sK56,nil),
    inference(definition_unfolding,[],[f553,f551]) ).

fof(f559,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f548,f551]) ).

fof(f560,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

fof(f562,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f356]) ).

fof(f580,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f495]) ).

cnf(c_54,plain,
    ( ~ ssList(app(X0,cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f438]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f470]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f580]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f521]) ).

cnf(c_220,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(sK51(X0)) ),
    inference(cnf_transformation,[],[f520]) ).

cnf(c_221,plain,
    ( ~ ssList(X0)
    | tl(X0) = sK52(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f523]) ).

cnf(c_222,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(sK52(X0)) ),
    inference(cnf_transformation,[],[f522]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f525]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f528]) ).

cnf(c_247,negated_conjecture,
    ~ neq(sK55,nil),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_248,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK56
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | app(X1,cons(X0,nil)) = sK55 ),
    inference(cnf_transformation,[],[f554]) ).

cnf(c_249,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_252,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_253,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_303,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_3222,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).

cnf(c_3223,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3222]) ).

cnf(c_3224,plain,
    sK55 = nil,
    inference(global_subsumption_just,[status(thm)],[c_3223,c_253,c_141,c_3223]) ).

cnf(c_3240,plain,
    ( nil != nil
    | sK56 != sK55 ),
    inference(resolution_lifted,[status(thm)],[c_247,c_249]) ).

cnf(c_3241,plain,
    sK56 != sK55,
    inference(global_subsumption_just,[status(thm)],[c_3240,c_141,c_195,c_303,c_3240]) ).

cnf(c_6057,plain,
    nil != sK56,
    inference(light_normalisation,[status(thm)],[c_3241,c_3224]) ).

cnf(c_7060,plain,
    ( app(cons(X0,nil),X1) != sK56
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | app(X1,cons(X0,nil)) = nil ),
    inference(light_normalisation,[status(thm)],[c_248,c_3224]) ).

cnf(c_17737,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_252,c_219]) ).

cnf(c_17738,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_17737,c_6057]) ).

cnf(c_17895,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_252,c_221]) ).

cnf(c_17896,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_17895,c_6057]) ).

cnf(c_18032,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_17738,c_220]) ).

cnf(c_18033,plain,
    ssItem(hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_18032,c_6057,c_252]) ).

cnf(c_18058,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_17896,c_222]) ).

cnf(c_18059,plain,
    ssList(tl(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_18058,c_6057,c_252]) ).

cnf(c_20159,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_252,c_224]) ).

cnf(c_20162,plain,
    cons(hd(sK56),tl(sK56)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_20159,c_6057]) ).

cnf(c_20368,plain,
    ( ~ ssList(X0)
    | app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
    inference(superposition,[status(thm)],[c_18033,c_227]) ).

cnf(c_21080,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
    inference(superposition,[status(thm)],[c_18059,c_20368]) ).

cnf(c_21082,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = sK56,
    inference(light_normalisation,[status(thm)],[c_21080,c_20162]) ).

cnf(c_24194,plain,
    ( ~ memberP(nil,hd(sK56))
    | ~ ssItem(hd(sK56)) ),
    inference(instantiation,[status(thm)],[c_171]) ).

cnf(c_24574,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = nil ),
    inference(superposition,[status(thm)],[c_21082,c_7060]) ).

cnf(c_24581,plain,
    app(tl(sK56),cons(hd(sK56),nil)) = nil,
    inference(forward_subsumption_resolution,[status(thm)],[c_24574,c_18059,c_18033]) ).

cnf(c_25311,plain,
    ( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | memberP(nil,hd(sK56)) ),
    inference(superposition,[status(thm)],[c_24581,c_54]) ).

cnf(c_25353,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | memberP(nil,hd(sK56)) ),
    inference(light_normalisation,[status(thm)],[c_25311,c_24581]) ).

cnf(c_25354,plain,
    memberP(nil,hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_25353,c_141,c_18059,c_18033]) ).

cnf(c_25357,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_25354,c_24194,c_18033]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC211+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 15:19:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.89/1.66  % SZS status Started for theBenchmark.p
% 7.89/1.66  % SZS status Theorem for theBenchmark.p
% 7.89/1.66  
% 7.89/1.66  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.89/1.66  
% 7.89/1.66  ------  iProver source info
% 7.89/1.66  
% 7.89/1.66  git: date: 2023-05-31 18:12:56 +0000
% 7.89/1.66  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.89/1.66  git: non_committed_changes: false
% 7.89/1.66  git: last_make_outside_of_git: false
% 7.89/1.66  
% 7.89/1.66  ------ Parsing...
% 7.89/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.89/1.66  
% 7.89/1.66  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 5  sf_s  rm: 5 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 7.89/1.66  
% 7.89/1.66  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.89/1.66  
% 7.89/1.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.89/1.66  ------ Proving...
% 7.89/1.66  ------ Problem Properties 
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  clauses                                 184
% 7.89/1.66  conjectures                             1
% 7.89/1.66  EPR                                     52
% 7.89/1.66  Horn                                    116
% 7.89/1.66  unary                                   19
% 7.89/1.66  binary                                  40
% 7.89/1.66  lits                                    625
% 7.89/1.66  lits eq                                 82
% 7.89/1.66  fd_pure                                 0
% 7.89/1.66  fd_pseudo                               0
% 7.89/1.66  fd_cond                                 21
% 7.89/1.66  fd_pseudo_cond                          14
% 7.89/1.66  AC symbols                              0
% 7.89/1.66  
% 7.89/1.66  ------ Schedule dynamic 5 is on 
% 7.89/1.66  
% 7.89/1.66  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  ------ 
% 7.89/1.66  Current options:
% 7.89/1.66  ------ 
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  ------ Proving...
% 7.89/1.66  
% 7.89/1.66  
% 7.89/1.66  % SZS status Theorem for theBenchmark.p
% 7.89/1.66  
% 7.89/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.89/1.66  
% 7.89/1.67  
%------------------------------------------------------------------------------